Description: Half of a number is zero iff the number is zero. (Contributed by NM, 20-Apr-2006)
Ref | Expression | ||
---|---|---|---|
Assertion | half0 | |- ( A e. CC -> ( ( A / 2 ) = 0 <-> A = 0 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn | |- 2 e. CC |
|
2 | 2ne0 | |- 2 =/= 0 |
|
3 | diveq0 | |- ( ( A e. CC /\ 2 e. CC /\ 2 =/= 0 ) -> ( ( A / 2 ) = 0 <-> A = 0 ) ) |
|
4 | 1 2 3 | mp3an23 | |- ( A e. CC -> ( ( A / 2 ) = 0 <-> A = 0 ) ) |